too few runs. Another consequence of the belief in local representativeness is
the well-known gambler’s fallacy. After observing a long run of red on the
roulette wheel ,for example ,most people erroneously believe that black is now
due ,presumably because the occurence of black will result in a more represen-
tative sequence than the occurrence of an additional red. Chance is commonly
viewed as a self-correcting process in which a deviation in one direction in-
duces a deviation in the opposite direction to restore the equilibrium. In fact,
deviations are not ‘‘corrected’’ as a chance process unfolds ,they are merely
diluted.
Misconceptions of chance are not limited to naive subjects. A study of the
statistical intuitions of experienced research psychologists (Tversky & Kahne-
man ,1971 ,2) revealed a lingering belief in what may be called the ‘‘law of
small numbers,’’ according to which even small samples are highly representa-
tive of the populations from which they are drawn. The responses of these
investigators reflected the expectation that a valid hypothesis about a popula-
tion will be represented by a statistically significant result in a sample—with
little regard for its size. As a consequence ,the researchers put too much faith in
the results of small samples and grossly overestimated the replicability of such
results. In the actual conduct of research ,this bias leads to the selection of
samples of inadequate size and to overinterpretation of findings.
Insensitivity to Predictability
People are sometimes called upon to make such numerical predictions as the
future value of a stock ,the demand for a commodity ,or the outcome of a foot-
ball game. Such predictions are often made by representativeness. For example,
suppose one is given a description of a company and is asked to predict its
future profit. If the description of the company is very favorable ,a very high
profit will appear most representative of that description; if the description is
mediocre ,a mediocre performance will appear most representative. The degree
to which the description is favorable is unaffected by the reliability of that de-
scription or by the degree to which it permits accurate prediction. Hence ,if
people predict solely in terms of the favorableness of the description ,their pre-
dictions will be insensitive to the reliability of the evidence and to the expected
accuracy of the prediction.
This mode of judgment violates the normative statistical theory in which the
extremeness and the range of predictions are controlled by considerations of
predictability. When predictability is nil ,the same prediction should be made
in all cases. For example ,if the descriptions of companies provide no informa-
tion relevant to profit ,then the same value (such as average profit) should be
predicted for all companies. If predictability is perfect ,of course ,the values
predicted will match the actual values and the range of predictions will equal
the range of outcomes. In general ,the higher the predictability ,the wider the
range of predicted values.
Several studies of numerical prediction have demonstrated that intuitive
predictions violate this rule ,and that subjects show little or no regard for con-
siderations of predictability (Kahneman & Tversky ,1973 ,4). In one of these
studies ,subjects were presented with several paragraphs ,each describing the
performance of a student teacher during a particular practice lesson. Some
Judgment under Uncertainty 589